Collective nonlinear dynamics and self-organization in decentralized power grids

Dirk Witthaut, Frank Hellmann, Jürgen Kurths, Stefan Kettemann, Hildegard Meyer-Ortmanns, and Marc Timme
Rev. Mod. Phys. 94, 015005 – Published 28 February 2022

Abstract

The ongoing transition to renewable energy supply comes with a restructuring of power grids, changing their effective interaction topologies, more and more strongly decentralizing them and substantially modifying their input, output, and response characteristics. All of these changes imply that power grids become increasingly affected by collective, nonlinear dynamic phenomena, structurally and dynamically more distributed and less predictable in space and time, more heterogeneous in its building blocks, and as a consequence less centrally controllable. Here cornerstone aspects of data-driven and mathematical modeling of collective dynamical phenomena emerging in real and model power grid networks by combining theories from nonlinear dynamics, stochastic processes and statistical physics, anomalous statistics, optimization, and graph theory are reviewed. The mathematical background required for adequate modeling and analysis approaches is introduced, an overview of power system models is given, and a range of collective dynamical phenomena are focused on, including synchronization and phase locking, flow (re)routing, Braess’s paradox, geometric frustration, and spreading and localization of perturbations and cascading failures, as well as the nonequilibrium dynamics of power grids, where fluctuations play a pivotal role.

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  • Received 30 April 2021

DOI:https://doi.org/10.1103/RevModPhys.94.015005

© 2022 American Physical Society

Physics Subject Headings (PhySH)

NetworksGeneral Physics

Authors & Affiliations

Dirk Witthaut*

  • Forschungszentrum Jülich, Institute for Energy and Climate Research (IEK-STE), 52428 Jülich, Germany and Institute for Theoretical Physics, University of Cologne, Köln 50937, Germany

Frank Hellmann

  • Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany

Jürgen Kurths

  • Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany, Humboldt University of Berlin, Berlin 12489, Germany, and Lobachevsky University of Nizhny Novgorod, Nizhnij Novgorod 603950, Russia

Stefan Kettemann§

  • Department of Physics and Earth Sciences and Department of Computer Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany and Division of Advanced Materials Science, POSTECH, San 31, Hyoja-dong, Nam-gu, Pohang 790-784, Republic of Korea

Hildegard Meyer-Ortmanns

  • Department of Physics and Earth Sciences, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany

Marc Timme

  • Chair for Network Dynamics, Center for Advancing Electronics (cfaed) and Institute for Theoretical Physics, Technical University of Dresden, 01062 Dresden, Germany and Lakeside Labs, 9020 Klagenfurt am Wörthersee, Austria

  • *d.witthaut@fz-juelich.de
  • hellmann@pik-potsdam.de
  • kurths@pik-potsdam.de
  • §s.kettemann@jacobs-university.de
  • h.ortmanns@jacobs-university.de
  • marc.timme@tu-dresden.de

Article Text

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Vol. 94, Iss. 1 — January - March 2022

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